Subcritical patterns and dissipative solitons due to intracavity photonic crystals

Manipulation of the bifurcation structure of nonlinear optical systems via intracavity photonic crystals is demonstrated. In particular, subcritical regions between spatially periodic states are stabilized by modulations of the material's refractive index. An family of dissipative solitons within this bistability range due to the intracavity photonic crystal is identified and characterized in both one and two transverse dimensions. Nontrivial snaking of the modulated-cavity soliton solutions is also presented

Phase-space structure of two-dimensional excitable localized structures

In this work we characterize in detail the bifurcation leading to an excitable regime mediated by localized structures in a dissipative nonlinear Kerr cavity with a homogeneous pump. Here we show how the route can be understood through a planar dynamical system in which a limit cycle becomes the homoclinic orbit of a saddle point (saddle-loop bifurcation). The whole picture is unveiled, and the mechanism by which this reduction occurs from the full infinite-dimensional dynamical system is studied. Finally, it is shown that the bifurcation leads to an excitability regime, under the application of suitable perturbations. Excitability is an emergent property for this system, as it emerges from the spatial dependence since the system does not exhibit any excitable behavior locally.Comment: 10 pages, 9 figure

Self-pulsing dynamics in a cavity soliton laser

The dynamics of a broad-area vertical-cavity surface-emitting laser (VCSEL) with frequency-selective feedback supporting bistable spatial solitons is analyzed experimentally and theoretically. The transient dynamics of a switch-on of a soliton induced by an external optical pulse shows strong self-pulsing at the external-cavity round-trip time with at least ten modes excited. The numerical analysis indicates an even broader bandwidth and a transient sweep of the center frequency. It is argued that mode-locking of spatial solitons is an interesting and viable way to achieve three-dimensional, spatio-temporal self-localization and that the transients observed are preliminary indications of a transient cavity light bullet in the dynamics, though on a non negligible background

Letters betweenClara Firth and W. J. Kerr

Letters concerning a position in the department of shorthand and typewriting at Utah Agricultural College

Effects of a localized beam on the dynamics of excitable cavity solitons

We study the dynamical behavior of dissipative solitons in an optical cavity filled with a Kerr medium when a localized beam is applied on top of the homogeneous pumping. In particular, we report on the excitability regime that cavity solitons exhibits which is emergent property since the system is not locally excitable. The resulting scenario differs in an important way from the case of a purely homogeneous pump and now two different excitable regimes, both Class I, are shown. The whole scenario is presented and discussed, showing that it is organized by three codimension-2 points. Moreover, the localized beam can be used to control important features, such as the excitable threshold, improving the possibilities for the experimental observation of this phenomenon.Comment: 9 Pages, 12 figure

Frequency and phase locking of laser cavity solitons

Self-localized states or dissipative solitons have the freedom of translation in systems with a homogeneous background. When compared to cavity solitons in coherently driven nonlinear optical systems, laser cavity solitons have the additional freedom of the optical phase. We explore the consequences of this additional Goldstone mode and analyse experimentally and numerically frequency and phase locking of laser cavity solitons in a vertical-cavity surface-emitting laser with frequency-selective feedback. Due to growth-related variations of the cavity resonance, the translational symmetry is usually broken in real devices. Pinning to different defects means that separate laser cavity solitons have different frequencies and are mutually incoherent. If two solitons are close to each other, however, their interaction leads to synchronization due to phase and frequency locking with strong similarities to the Adler-scenario of coupled oscillators

From one- to two-dimensional solitons in the Ginzburg-Landau model of lasers with frequency selective feedback

We use the cubic complex Ginzburg-Landau equation coupled to a dissipative linear equation as a model of lasers with an external frequency-selective feedback. It is known that the feedback can stabilize the one-dimensional (1D) self-localized mode. We aim to extend the analysis to 2D stripe-shaped and vortex solitons. The radius of the vortices increases linearly with their topological charge, $m$, therefore the flat-stripe soliton may be interpreted as the vortex with $m=\infty$, while vortex solitons can be realized as stripes bent into rings. The results for the vortex solitons are applicable to a broad class of physical systems. There is a qualitative agreement between our results and those recently reported for models with saturable nonlinearity.Comment: Submitted to PR

Drifting instabilities of cavity solitons in vertical cavity surface-emitting lasers with frequency selective feedback

In this paper we study the formation and dynamics of self-propelled cavity solitons (CSs) in a model for vertical cavity surface-emitting lasers (VCSELs) subjected to external frequency selective feedback (FSF), and build their bifurcation diagram for the case where carrier dynamics is eliminated. For low pump currents, we find that they emerge from the modulational instability point of the trivial solution, where traveling waves with a critical wavenumber are formed. For large currents, the branch of self-propelled solitons merges with the branch of resting solitons via a pitchfork bifurcation. We also show that a feedback phase variation of 2\pi can transform a CS (whether resting or moving) into a different one associated to an adjacent longitudinal external cavity mode. Finally, we investigate the influence of the carrier dynamics, relevant for VCSELs. We find and analyze qualitative changes in the stability properties of resting CSs when increasing the carrier relaxation time. In addition to a drifting instability of resting CSs, a new kind of instability appears for certain ranges of carrier lifetime, leading to a swinging motion of the CS center position. Furthermore, for carrier relaxation times typical of VCSELs the system can display multistability of CSs.Comment: 11 pages, 12 figure

Spatial correlations in hexagons generated via a Kerr nonlinearity

We consider the hexagonal pattern forming in the cross-section of an optical beam produced by a Kerr cavity, and we study the quantum correlations characterizing this structure. By using arguments related to the symmetry broken by the pattern formation, we identify a complete scenario of six-mode entanglement. Five independent phase quadratures combinations, connecting the hexagonal modes, are shown to exhibit sub-shot-noise fluctuations. By means of a non-linear quantum calculation technique, quantum correlations among the mode photon numbers are demonstrated and calculated.Comment: ReVTeX file, 20 pages, 7 eps figure